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<li class="navelem"><a class="el" href="dir_d44c64559bbebec7f509842c48db8b23.html">include</a></li><li class="navelem"><a class="el" href="dir_9d8b5820aeddb56054d6182409bbdf51.html">cpp0x</a></li>  </ul>
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<div class="title">algebra.h</div>  </div>
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<div class="fragment"><div class="line"><a name="l00001"></a><span class="lineno">    1</span>&#160;<span class="preprocessor">#ifndef __GAALET_ALGEBRA_H</span></div>
<div class="line"><a name="l00002"></a><span class="lineno">    2</span>&#160;<span class="preprocessor">#define __GAALET_ALGEBRA_H</span></div>
<div class="line"><a name="l00003"></a><span class="lineno">    3</span>&#160;</div>
<div class="line"><a name="l00004"></a><span class="lineno">    4</span>&#160;<span class="preprocessor">#include &quot;multivector.h&quot;</span></div>
<div class="line"><a name="l00005"></a><span class="lineno">    5</span>&#160;<span class="preprocessor">#include &quot;utility.h&quot;</span></div>
<div class="line"><a name="l00006"></a><span class="lineno">    6</span>&#160;</div>
<div class="line"><a name="l00007"></a><span class="lineno">    7</span>&#160;<span class="keyword">namespace </span><a class="code" href="namespacegaalet.html">gaalet</a></div>
<div class="line"><a name="l00008"></a><span class="lineno">    8</span>&#160;{</div>
<div class="line"><a name="l00009"></a><span class="lineno">    9</span>&#160;</div>
<div class="line"><a name="l00010"></a><span class="lineno">   10</span>&#160;<span class="comment">//metric of multivector</span></div>
<div class="line"><a name="l00011"></a><span class="lineno">   11</span>&#160;<span class="comment">// --- only definable by signature yet</span></div>
<div class="line"><a name="l00012"></a><span class="lineno">   12</span>&#160;<span class="comment">// --- interface may change in order to allow for a general metric tensor</span></div>
<div class="line"><a name="l00013"></a><span class="lineno">   13</span>&#160;<span class="keyword">template</span>&lt;<span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> P, <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> Q, <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> R=0&gt;</div>
<div class="line"><a name="l00014"></a><span class="lineno"><a class="line" href="structgaalet_1_1signature.html">   14</a></span>&#160;<span class="keyword">struct </span><a class="code" href="structgaalet_1_1signature.html">signature</a></div>
<div class="line"><a name="l00015"></a><span class="lineno">   15</span>&#160;{</div>
<div class="line"><a name="l00016"></a><span class="lineno">   16</span>&#160;   <span class="keyword">static</span> <span class="keyword">const</span> <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> p = P;</div>
<div class="line"><a name="l00017"></a><span class="lineno">   17</span>&#160;   <span class="keyword">static</span> <span class="keyword">const</span> <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> q = Q;</div>
<div class="line"><a name="l00018"></a><span class="lineno">   18</span>&#160;   <span class="keyword">static</span> <span class="keyword">const</span> <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> r = R;</div>
<div class="line"><a name="l00019"></a><span class="lineno">   19</span>&#160;   <span class="keyword">static</span> <span class="keyword">const</span> <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> dimension = P+Q+R;</div>
<div class="line"><a name="l00020"></a><span class="lineno">   20</span>&#160;</div>
<div class="line"><a name="l00021"></a><span class="lineno">   21</span>&#160;   <span class="keyword">static</span> <span class="keyword">const</span> conf_t signature_bitmap = (<a class="code" href="structgaalet_1_1Power.html">Power&lt;2, Q&gt;::value</a>-1)&lt;&lt;P;</div>
<div class="line"><a name="l00022"></a><span class="lineno">   22</span>&#160;   <span class="keyword">static</span> <span class="keyword">const</span> conf_t degenerate_bitmap = (<a class="code" href="structgaalet_1_1Power.html">Power&lt;2, R&gt;::value</a>-1)&lt;&lt;(P+Q);</div>
<div class="line"><a name="l00023"></a><span class="lineno">   23</span>&#160;};</div>
<div class="line"><a name="l00024"></a><span class="lineno">   24</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> ML, <span class="keyword">typename</span> MR&gt;</div>
<div class="line"><a name="l00025"></a><span class="lineno"><a class="line" href="structgaalet_1_1metric__combination__traits.html">   25</a></span>&#160;<span class="keyword">struct </span><a class="code" href="structgaalet_1_1metric__combination__traits.html">metric_combination_traits</a>;</div>
<div class="line"><a name="l00026"></a><span class="lineno">   26</span>&#160;</div>
<div class="line"><a name="l00027"></a><span class="lineno">   27</span>&#160;<span class="comment">//combination of signature metrics -&gt; negative signature dominant</span></div>
<div class="line"><a name="l00028"></a><span class="lineno">   28</span>&#160;<span class="keyword">template</span>&lt;<span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> PL, <span class="keywordtype">unsigned</span> QL, <span class="keywordtype">unsigned</span> RL, <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> PR, <span class="keywordtype">unsigned</span> QR, <span class="keywordtype">unsigned</span> RR&gt;</div>
<div class="line"><a name="l00029"></a><span class="lineno"><a class="line" href="structgaalet_1_1metric__combination__traits_3_01signature_3_01PL_00_01QL_00_01RL_01_4_00_01signae66c4fed3a29676557db6c7702aaa4d6.html">   29</a></span>&#160;<span class="keyword">struct </span><a class="code" href="structgaalet_1_1metric__combination__traits.html">metric_combination_traits</a>&lt;<a class="code" href="structgaalet_1_1signature.html">signature</a>&lt;PL, QL, RL&gt;, <a class="code" href="structgaalet_1_1signature.html">signature</a>&lt;PR, QR, RR&gt;&gt;</div>
<div class="line"><a name="l00030"></a><span class="lineno">   30</span>&#160;{</div>
<div class="line"><a name="l00031"></a><span class="lineno">   31</span>&#160;   static_assert(PL==PR || (PL&lt;PR &amp;&amp; QL==0) || (PR&lt;PL &amp;&amp; QR==0),</div>
<div class="line"><a name="l00032"></a><span class="lineno">   32</span>&#160;                 <span class="stringliteral">&quot;Combination of different metrics: different number of positive signatures&quot;</span>);</div>
<div class="line"><a name="l00033"></a><span class="lineno">   33</span>&#160;   static_assert(PL+QL==PR+QR || (PL+QL&lt;PR+QR &amp;&amp; RL==0) || (PR+QR&lt;PL+QL &amp;&amp; RR==0),</div>
<div class="line"><a name="l00034"></a><span class="lineno">   34</span>&#160;                 <span class="stringliteral">&quot;Combination of different metrics: different number of positive plus negative signatures&quot;</span>);</div>
<div class="line"><a name="l00035"></a><span class="lineno">   35</span>&#160;   <span class="keyword">static</span> <span class="keyword">const</span> <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> P = (PL&gt;PR) ? PL : PR;</div>
<div class="line"><a name="l00036"></a><span class="lineno">   36</span>&#160;   <span class="keyword">static</span> <span class="keyword">const</span> <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> Q = (QL&gt;QR) ? QL : QR;</div>
<div class="line"><a name="l00037"></a><span class="lineno">   37</span>&#160;   <span class="keyword">static</span> <span class="keyword">const</span> <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> R = (RL&gt;RR) ? RL : RR;</div>
<div class="line"><a name="l00038"></a><span class="lineno">   38</span>&#160;</div>
<div class="line"><a name="l00039"></a><span class="lineno">   39</span>&#160;   <span class="keyword">typedef</span> <a class="code" href="structgaalet_1_1signature.html">signature&lt;P, Q, R&gt;</a> <a class="code" href="structgaalet_1_1signature.html">metric</a>;</div>
<div class="line"><a name="l00040"></a><span class="lineno">   40</span>&#160;   <span class="comment">//typedef ::gaalet::metric&lt;SL | SR&gt; metric;</span></div>
<div class="line"><a name="l00041"></a><span class="lineno">   41</span>&#160;};</div>
<div class="line"><a name="l00042"></a><span class="lineno">   42</span>&#160;</div>
<div class="line"><a name="l00043"></a><span class="lineno">   43</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> M, <span class="keyword">typename</span> T = default_element_t&gt;</div>
<div class="line"><a name="l00044"></a><span class="lineno"><a class="line" href="structgaalet_1_1algebra.html">   44</a></span>&#160;<span class="keyword">struct </span><a class="code" href="structgaalet_1_1algebra.html">algebra</a></div>
<div class="line"><a name="l00045"></a><span class="lineno">   45</span>&#160;{</div>
<div class="line"><a name="l00046"></a><span class="lineno">   46</span>&#160;   <span class="keyword">typedef</span> M metric;</div>
<div class="line"><a name="l00047"></a><span class="lineno">   47</span>&#160;</div>
<div class="line"><a name="l00048"></a><span class="lineno">   48</span>&#160;   <span class="keyword">typedef</span> T element_t;</div>
<div class="line"><a name="l00049"></a><span class="lineno">   49</span>&#160;</div>
<div class="line"><a name="l00050"></a><span class="lineno">   50</span>&#160;   <span class="comment">//no cpp0x template aliases supported by gcc yet</span></div>
<div class="line"><a name="l00051"></a><span class="lineno">   51</span>&#160;   <span class="comment">/*template&lt;conf_t head, conf_t... tail&gt;</span></div>
<div class="line"><a name="l00052"></a><span class="lineno">   52</span>&#160;<span class="comment">   using mv = multivector&lt;typename insert_element&lt;head, typename mv&lt;tail...&gt;::clist&gt;::clist&gt;;</span></div>
<div class="line"><a name="l00053"></a><span class="lineno">   53</span>&#160;<span class="comment"></span></div>
<div class="line"><a name="l00054"></a><span class="lineno">   54</span>&#160;<span class="comment">   template&lt;&gt;</span></div>
<div class="line"><a name="l00055"></a><span class="lineno">   55</span>&#160;<span class="comment">   using mv = multivector&lt;cl_null&gt;;*/</span></div>
<div class="line"><a name="l00056"></a><span class="lineno">   56</span>&#160;</div>
<div class="line"><a name="l00057"></a><span class="lineno">   57</span>&#160;   <span class="comment">//multivector configuration elements unpacking</span></div>
<div class="line"><a name="l00058"></a><span class="lineno">   58</span>&#160;   <span class="keyword">template</span>&lt;conf_t... elements&gt;</div>
<div class="line"><a name="l00059"></a><span class="lineno"><a class="line" href="structgaalet_1_1algebra_1_1mv.html">   59</a></span>&#160;   <span class="keyword">struct </span><a class="code" href="structgaalet_1_1algebra_1_1mv.html">mv</a>;</div>
<div class="line"><a name="l00060"></a><span class="lineno">   60</span>&#160;   <span class="keyword">template</span>&lt;conf_t head, conf_t... tail&gt;</div>
<div class="line"><a name="l00061"></a><span class="lineno"><a class="line" href="structgaalet_1_1algebra_1_1mv_3_01head_00_01tail_8_8_8_01_4.html">   61</a></span>&#160;   <span class="keyword">struct </span><a class="code" href="structgaalet_1_1algebra_1_1mv.html">mv</a>&lt;head, tail...&gt;</div>
<div class="line"><a name="l00062"></a><span class="lineno">   62</span>&#160;   {</div>
<div class="line"><a name="l00063"></a><span class="lineno">   63</span>&#160;      <span class="keyword">typedef</span> <a class="code" href="structgaalet_1_1multivector.html">multivector</a>&lt;<span class="keyword">typename</span> <a class="code" href="structgaalet_1_1insert__element.html">insert_element</a>&lt;head, <span class="keyword">typename</span> <a class="code" href="structgaalet_1_1algebra_1_1mv.html">mv</a>&lt;tail...&gt;::type::clist&gt;::clist, metric, element_t&gt; <a class="code" href="structgaalet_1_1multivector.html">type</a>;</div>
<div class="line"><a name="l00064"></a><span class="lineno">   64</span>&#160;   };</div>
<div class="line"><a name="l00065"></a><span class="lineno">   65</span>&#160;   <span class="keyword">template</span>&lt;conf_t head&gt;</div>
<div class="line"><a name="l00066"></a><span class="lineno"><a class="line" href="structgaalet_1_1algebra_1_1mv_3_01head_01_4.html">   66</a></span>&#160;   <span class="keyword">struct </span><a class="code" href="structgaalet_1_1algebra_1_1mv.html">mv</a>&lt;head&gt;</div>
<div class="line"><a name="l00067"></a><span class="lineno">   67</span>&#160;   {</div>
<div class="line"><a name="l00068"></a><span class="lineno">   68</span>&#160;      <span class="keyword">typedef</span> <a class="code" href="structgaalet_1_1multivector.html">multivector&lt;configuration_list&lt;head, cl_null&gt;</a>, metric, element_t&gt; <a class="code" href="structgaalet_1_1multivector.html">type</a>;</div>
<div class="line"><a name="l00069"></a><span class="lineno">   69</span>&#160;   };</div>
<div class="line"><a name="l00070"></a><span class="lineno">   70</span>&#160;};</div>
<div class="line"><a name="l00071"></a><span class="lineno">   71</span>&#160;</div>
<div class="line"><a name="l00072"></a><span class="lineno">   72</span>&#160;<span class="comment">//default multivector: euclidean space (in signature bitmap, P part won&#39;t matter if Q part equals zero)</span></div>
<div class="line"><a name="l00073"></a><span class="lineno">   73</span>&#160;<span class="keyword">template</span>&lt;conf_t... elements&gt;</div>
<div class="line"><a name="l00074"></a><span class="lineno"><a class="line" href="structgaalet_1_1mv.html">   74</a></span>&#160;<span class="keyword">struct </span><a class="code" href="structgaalet_1_1mv.html">mv</a></div>
<div class="line"><a name="l00075"></a><span class="lineno">   75</span>&#160;{</div>
<div class="line"><a name="l00076"></a><span class="lineno">   76</span>&#160;   <span class="keyword">typedef</span> <span class="keyword">typename</span> <a class="code" href="structgaalet_1_1algebra.html">algebra&lt;signature&lt;0,0&gt;</a>&gt;<a class="code" href="structgaalet_1_1mv.html">::mv</a>&lt;elements...&gt;::type type;</div>
<div class="line"><a name="l00077"></a><span class="lineno">   77</span>&#160;};</div>
<div class="line"><a name="l00078"></a><span class="lineno">   78</span>&#160;</div>
<div class="line"><a name="l00079"></a><span class="lineno">   79</span>&#160;</div>
<div class="line"><a name="l00080"></a><span class="lineno">   80</span>&#160;<span class="comment">//Algebra definitions</span></div>
<div class="line"><a name="l00081"></a><span class="lineno">   81</span>&#160;<span class="comment">//typedef algebra&lt;signature&lt;4,1&gt;&gt; cm;</span></div>
<div class="line"><a name="l00082"></a><span class="lineno"><a class="line" href="structgaalet_1_1cm.html">   82</a></span>&#160;<span class="keyword">struct </span><a class="code" href="structgaalet_1_1cm.html">cm</a> {</div>
<div class="line"><a name="l00083"></a><span class="lineno">   83</span>&#160;   typedef ::gaalet::algebra&lt;signature&lt;4,1&gt;&gt; <a class="code" href="structgaalet_1_1algebra.html">algebra</a>;</div>
<div class="line"><a name="l00084"></a><span class="lineno">   84</span>&#160;</div>
<div class="line"><a name="l00085"></a><span class="lineno">   85</span>&#160;   <span class="keyword">template</span>&lt;conf_t... elements&gt;</div>
<div class="line"><a name="l00086"></a><span class="lineno"><a class="line" href="structgaalet_1_1cm_1_1mv.html">   86</a></span>&#160;   <span class="keyword">struct </span><a class="code" href="structgaalet_1_1cm_1_1mv.html">mv</a></div>
<div class="line"><a name="l00087"></a><span class="lineno">   87</span>&#160;   {</div>
<div class="line"><a name="l00088"></a><span class="lineno">   88</span>&#160;      <span class="keyword">typedef</span> <span class="keyword">typename</span> <a class="code" href="structgaalet_1_1algebra_1_1mv.html">algebra::mv</a>&lt;elements...&gt;::type type;</div>
<div class="line"><a name="l00089"></a><span class="lineno">   89</span>&#160;   };</div>
<div class="line"><a name="l00090"></a><span class="lineno">   90</span>&#160;};</div>
<div class="line"><a name="l00091"></a><span class="lineno">   91</span>&#160;</div>
<div class="line"><a name="l00092"></a><span class="lineno">   92</span>&#160;</div>
<div class="line"><a name="l00093"></a><span class="lineno">   93</span>&#160;} <span class="comment">//end namespace gaalet</span></div>
<div class="line"><a name="l00094"></a><span class="lineno">   94</span>&#160;</div>
<div class="line"><a name="l00095"></a><span class="lineno">   95</span>&#160;<span class="preprocessor">#endif</span></div>
<div class="ttc" id="structgaalet_1_1multivector_html"><div class="ttname"><a href="structgaalet_1_1multivector.html">gaalet::multivector</a></div><div class="ttdef"><b>Definition:</b> multivector.h:19</div></div>
<div class="ttc" id="structgaalet_1_1cm_1_1mv_html"><div class="ttname"><a href="structgaalet_1_1cm_1_1mv.html">gaalet::cm::mv</a></div><div class="ttdef"><b>Definition:</b> algebra.h:86</div></div>
<div class="ttc" id="namespacegaalet_html"><div class="ttname"><a href="namespacegaalet.html">gaalet</a></div><div class="ttdef"><b>Definition:</b> addition.h:4</div></div>
<div class="ttc" id="structgaalet_1_1algebra_1_1mv_html"><div class="ttname"><a href="structgaalet_1_1algebra_1_1mv.html">gaalet::algebra::mv</a></div><div class="ttdef"><b>Definition:</b> algebra.h:59</div></div>
<div class="ttc" id="structgaalet_1_1cm_html"><div class="ttname"><a href="structgaalet_1_1cm.html">gaalet::cm</a></div><div class="ttdef"><b>Definition:</b> algebra.h:82</div></div>
<div class="ttc" id="structgaalet_1_1metric__combination__traits_html"><div class="ttname"><a href="structgaalet_1_1metric__combination__traits.html">gaalet::metric_combination_traits</a></div><div class="ttdef"><b>Definition:</b> algebra.h:25</div></div>
<div class="ttc" id="structgaalet_1_1insert__element_html"><div class="ttname"><a href="structgaalet_1_1insert__element.html">gaalet::insert_element</a></div><div class="ttdef"><b>Definition:</b> configuration_list.h:46</div></div>
<div class="ttc" id="structgaalet_1_1algebra_html"><div class="ttname"><a href="structgaalet_1_1algebra.html">gaalet::algebra</a></div><div class="ttdef"><b>Definition:</b> algebra.h:44</div></div>
<div class="ttc" id="structgaalet_1_1mv_html"><div class="ttname"><a href="structgaalet_1_1mv.html">gaalet::mv</a></div><div class="ttdef"><b>Definition:</b> algebra.h:74</div></div>
<div class="ttc" id="structgaalet_1_1signature_html"><div class="ttname"><a href="structgaalet_1_1signature.html">gaalet::signature</a></div><div class="ttdef"><b>Definition:</b> algebra.h:14</div></div>
<div class="ttc" id="structgaalet_1_1Power_html"><div class="ttname"><a href="structgaalet_1_1Power.html">gaalet::Power</a></div><div class="ttdef"><b>Definition:</b> utility.h:35</div></div>
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